why do we expand any periodic function by fourier series not by any other series?

Question

what is the use of fourier series

Answer 1

Because the intrinsic periodicity of the trigonometric functions. You can addapt the natural period 2 Pi by division for the correponding constants. But it is not the only solution. Elliptic functions, for instance, the inverses of elliptic integrals, are used to model double-periodic phenomena.

Answer 2

Would u attempt ur Hw , or at least post it in HW help rather than engineering